Problem: Solve for $x$ and $y$ using elimination. ${-3x-3y = -36}$ ${4x-5y = 3}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $3$ ${-12x-12y = -144}$ $12x-15y = 9$ Add the top and bottom equations together. $-27y = -135$ $\dfrac{-27y}{{-27}} = \dfrac{-135}{{-27}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-3x-3y = -36}\thinspace$ to find $x$ ${-3x - 3}{(5)}{= -36}$ $-3x-15 = -36$ $-3x-15{+15} = -36{+15}$ $-3x = -21$ $\dfrac{-3x}{{-3}} = \dfrac{-21}{{-3}}$ ${x = 7}$ You can also plug ${y = 5}$ into $\thinspace {4x-5y = 3}\thinspace$ and get the same answer for $x$ : ${4x - 5}{(5)}{= 3}$ ${x = 7}$